ANAHEIM, Calif. — The task is a monumental one. On Sunday, Clay Buchholz will be given the ball for his first career playoff start and asked to save the Red Sox’ season.

The Sox dropped the first two games to the Angels, and so face a win-or-go-home scenario when Buchholz takes the ball for Game 3 of the best-of-five American League Division Series. It is an enormous request to make of any pitcher, let alone one whose previous two Octobers were spent contemplating the disappointment of missed opportunities.

Then again, perhaps it is because of the dismay of the end of those past two seasons that the task of starting Game 3 — even with his team facing elimination — strikes Buchholz as so appealing. Finally, he has a chance to establish a reputation in October, rather than being relegated to the status of a playoff footnote.

“I’ve always liked pitching under pressure and all that stuff. I think every pitcher does,” Buchholz said shortly after his team’s 4-1 loss on Friday. “You want to be put into situations where, if you succeed, the feeling is that much better than any other time.

“[Being down, 0-2, in the series] definitely isn’t what you want, but I’ve had some ups and downs this year, starting off in Pawtucket and then finally getting up here,” he added. “This is where you want to be. This is a make-or-break situation. This is where you have those games where you know you have to win to give your team a chance to win.”

It is an opportunity three seasons in the making.

DISAPPOINTMENT, TAKE 1

In 2007, Buchholz earned a victory against the Angels in his big-league debut and then burst into national consciousness by throwing a no-hitter in his second big-league start. The right-hander stood poised to be an X-factor in the playoffs.

Had he made the postseason roster, there is a good chance that the right-hander would have been called upon to replace Tim Wakefield in the rotation when a labrum tear forced the knuckleballer to cede his Game 4 start against the Rockies. On that national stage, he could have instantly cemented his status as the next big thing for the Red Sox.

Instead, Buchholz was shut down toward the end of September because the Sox were concerned that weakness in his right shoulder could jeopardize his long-term health if he continued pitching. He watched the World Series from Pensacola, Fla., where he was working out at an Athletes Performance facility.

Then 23, Buchholz recalls “bittersweet” emotions while watching the Sox sweep their way to a title. He was happy for Jon Lester — who started and won Game 4 — and the team on which his prospect star had flickered, but knew that he’d missed a potentially career-defining opportunity.

“The last game, I thought, ‘Wow, I wish I was there,’ ” Buchholz said. “But things happened that didn’t allow me to do that. It made me want to work harder toward a goal to be that guy on the roster, pitching Game 3 or Game 4, which happened to be the deciding game of the World Series.

“It was something that was hard to watch in the sense that I thought I could be there and maybe should be there if things went maybe a little different. But the way things went, everything happens for a reason.”

In this case, that reason was developing a between-starts routine and a shoulder strengthening and conditioning regimen for the young pitcher. The disappointment of his non-involvement in the playoff run helped Buchholz to lay what he and the Sox hope will be the physical foundation for long-term success.

Even after he implemented a program to ensure that he would not be too frail to succeed, however, Buchholz had more to do to put himself in position to handle major league competition.

DISAPPOINTMENT, TAKE 2

One year after that banishment to Pensacola, Buchholz was once again left to follow his team’s postseason from afar. This time, it was in the Arizona Fall League for entirely different reasons.

In ’07, Buchholz was too frail for the postseason. The Sox believed he was capable of succeeding in October, but they feared the long-term cost. In 2008, the physical limitations were behind the pitcher, but there was no sense that he could execute in a fashion that would prove helpful in the postseason.

Instead, after he went 2-9 with a 6.75 ERA, the Sox sent him down to Double A. There were a number of issues that they wanted Buchholz to work on, among them:

— Becoming less reliant on his changeup and curve, and throwing his fastball with greater conviction.

— Improving his focus on the opposing hitter, rather than being distracted by any batters on first base.

— Taking less time to dwell on each pitch, and learning to work more efficiently and with greater conviction.

And so, Buchholz was in Arizona as the Sox made their journey through the postseason. Once again, Buchholz was left to watch Lester — a pitcher who, at the start of 2008, was considered a lesser prospect than Buchholz — pitch in the Sox’ most important game of the year.

There was frustration, but also resignation.

“I knew I didn’t deserve to be on the roster,” Buchholz said. “Obviously, I wished I was there. I wish I would have gotten an opportunity to do that. But knowing that I hadn’t pitched well enough to prove that I belonged, I think [the minors] was something I needed to do.

“Last year was a reality check for me, to say I’ve got to work a lot harder to get to that point where I want to stay a long time,” he continued. It wasn’t the easiest thing for me [to watch the playoffs], knowing that the door was open for me to be in the driver’s seat. All I had to do was pitch and do the things I’d done throughout my professional career. It was bitter at first. [But] I look at it and say I put myself in the position to not be there.”

JOCKEYING FOR POSITION

Yet for the second straight year, Buchholz treated disappointment constructively. He tried to implement the changes that the Sox outlined, a process that gained true definition this year during spring training.

Pitching coach John Farrell and manager Terry Francona approached the right-hander at the beginning of the spring. In exhibition games, they wanted to see him employ a different plan of attack than the breaking ball-heavy desperation that was constantly on display down the stretch in ’08.

For innings and outings at a time, Buchholz was asked to pocket his curve and change, and instead fire his four- and two-seam fastball to both sides of the plate, and to complement that with a hard slider.

“When needed, a well-located fastball is still as good a pitch as there is in the major leagues,” Farrell explained. “To me, the additon of his two-seamer has probably been the biggest key to his overall confidence as a pitcher, knowing that if he’s in a fastball count, he still has enough life and movement to get the ball off the bat head.

“As he became comfortable with that, his secondary pitches have been brought back into the mix with more usage,” Farrell added. “What we’re seeing is the key, not only the transition to the major leagues on a consistent basis, but the use of a full complement of a four-pitch mix that has allowed him to be unpredictable.”

That allowed Buchholz to dominate this year in the minors, where he went 7-2 with a 2.36 ERA in Triple A. Even so, he couldn’t find a way into the big-league rotation.

Finally, the Sox felt it important to bring him up to the majors, even if for a cameo. Buchholz wasn’t supposed to get anything more than a spot start. He was called up from the minors to make the first start of the second half for the Red Sox, and he delivered a solid 5-2/3 innings while allowing just one run for the win.

The Sox sent him back to Pawtucket following the game, but then the season took a dramatic turn, when Wakefield went down with a back injury that forced him to the disabled list. Buchholz was immediately brought back to the majors, and laid aggressive claim to a spot in the rotation.

In 16 games (coincidentally, the same number he threw in the majors in 2008), Buchholz went 7-4 with a 4.21 ERA. He proved particularly impressive during a 10-start stretch from Aug. 8 through Sept. 24, going 6-2 with a 2.37 ERA, in the process showing that he could hold his own while pitching against the likes of CC Sabathia, Justin Verlander and Roy Halladay.

Facing those three pitchers, Buchholz threw quality starts in each of his outings, keeping the Sox in the game on nights when their offense could muster nothing.

“Those guys are the best guys in the game, and I threw pretty well against them,” Buchholz said. “It was reassuring for me.”

It was reassuring, too, for the Sox. Suddenly, the notion that the wide-eyed junior college product would be overwhelmed by the weight of a playoff race or the postseason could be downplayed.

That is not to say that the season has been without its glitches. Buchholz stumbled in his final two starts, getting tagged for 13 runs and six homers in just eight innings. In those outings, he seemed to be shaking off catcher Victor Martinez to a fault, once again overthinking his plan of attack.

He recognizes the need to “throw pitches with conviction” in his postseason unveiling. If he does so, and attacks the strike zone with a four-pitch mix (mid-90s fastball, slider, curve, change), he can unbalance even playoff-caliber lineups, something that the Sox will need him to do on Sunday.

“I think we have a lot of confidence. He’s a guy who has pitched very well against good teams,” third baseman Mike Lowell said. “He has the ability to keep hitters off-balance. He has more than one plus pitch. We’re going to need him to have a good performance, obviously. We feel good about it, absolutely.”

Buchholz said that he pitched in some playoff circumstances in high school and college. He also took the mound in a Double-A playoff game last September. Even so, clearly he is operating on a different scale at this point.

And Buchholz insists that this latest challenge is welcome, even if it’s one for which he “definitely” will be nervous.

He has asked Josh Beckett and Lester about the differences between pitching in the regular season and the playoffs, and been told that words could not explain the distinction. Buchholz simply will have to learn on the fly, and find out what it means to pitch in the postseason based on personal experience.

He has seen that Beckett and Lester have minimized their own mistakes against the Angels, and yet both have suffered defeats. And so, he recognized, there is little forgiveness for missteps in October. There is undoubtedly pressure, but it is not unwelcome.

“Everybody wants to be under the pressure situations and pitch well and come out on top, and I think that’s what the playoffs is: It’s the five games that you have a chance to win to move on to the next round,” Buchholz said. “I feel like I’m ready for that point, I haven’t really been a part of one yet, but no better time than now.”

There is, after all, not only pressure but also excitement. Game 3 represents a chance for Buchholz not merely to experience the thrilling jitters of October, but also to show the progress that he has made over the previous seasons.

“I can get better. I can get a lot better. There’s still things I need to work on. But seeing how far it’s gone, how far it’s come from last year to right now, I know the work paid off and the adverse times paid off,” Buchholz said. “I know that every time I go out there, if I throw the pitches I want to throw and command them, I think that I have a chance to win.”

Now, the true measure of that statement will come to light in Game 3, at a time when a poor start will likely signal the end of the Sox’ 2009 season. It is later than he had anticipated the moment arriving, but it is also the case that Buchholz would not be in this position but for the struggles he faced in 2007 and 2008.

He has an opportunity to change the meaning of October, both for him and his career. A month that has seemed tainted by failure can now become one of the pitcher’s triumph. That quest starts on Sunday.